The Yankees’ refusal to go overboard for any free agents, be they from their own team or elsewhere, has them immersed in battles all over the continent and all over the diamond.

The Blue Jays “love” closer David Robertson, according to one industry source, and have engaged in dialogue with Robertson’s agent Scott Leventhal. And the Giants have “solid” interest in third baseman Chase Headley, according to a second source. FOX Sports’ Ken Rosenthal reported San Francisco’s pursuit of Headley had turned “aggressive.”

After finishing one game behind the Yankees in 2014, Toronto has joined Boston as the most active American League East teams to date this offseason. Already, as baseball officials arrive in San Diego on Sunday for the Winter Meetings, the Jays have signed former Yankees catcher Russell Martin to a five-year, $82-million contract and acquired third baseman Josh Donaldson (from Oakland) and outfielder Michael Saunders (from Seattle) in trades.

“Toronto and Boston have made some big moves, no doubt about it,” Yankees general manager Brian Cashman said Friday. “They’ve improved.”

Both teams are looking to do far more. Jon Heyman of CBS Sports first reported the Blue Jays’ consideration of Robertson, as Toronto’s bullpen faltered last season. However, whether the Jays will meet Robertson’s asking price of about $50 million over four years remains in question. Even some Toronto officials are skeptical that the club ultimately will land the Yankees’ closer of 2014, and the club also is very high on accomplished free-agent setup man Luke Gregerson.

Though the Yankees remain involved with their homegrown product Robertson, their signing of power lefty reliever Andrew Miller to a four-year, $36-million contract Friday diminishes their need for Robertson. The Yankees have been steadfast that they won’t give Robertson the years and dollars he wants — it’s notable the Yankees weren’t even the highest bidders for Miller. The Astros offered Miller four years and $40 million, and they also have pursued Robertson, although The Post’s George King reported last week that Houston officials are skeptical whether Robertson actually would come aboard.

Headley, meanwhile, charmed the Yankees with his half-season audition in pinstripes, yet the team might not guarantee more than three years to the third baseman. The Giants, looking to defend their third World Series title in five years, know they need an experienced bat to fill the void left by Pablo Sandoval’s departure to Boston, and their two open position are third base (which Sandoval played) and left field. Consequently, San Francisco also is interested in a reunion with former Yankee Melky Cabrera, whose previous tenure at AT&T Park concluded in 2012 with a suspension for a failed drug test.